Question: Let $f(x) = 5x^{2}-8x+3$. Where does this function intersect the x-axis (i.e. what are the roots or zeroes of $f(x)$ )?
Explanation: The function intersects the x-axis when $f(x) = 0$ , so you need to solve the equation: $5x^{2}-8x+3 = 0$ Use the quadratic formula to solve $ax^2 + bx + c = 0$ $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ $a = 5, b = -8, c = 3$ $ x = \dfrac{+ 8 \pm \sqrt{(-8)^{2} - 4 \cdot 5 \cdot 3}}{2 \cdot 5}$ $ x = \dfrac{8 \pm \sqrt{4}}{10}$ $ x = \dfrac{8 \pm 2}{10}$ $x =1,\frac{3}{5}$